A new and distinct variety of white flat peach tree denominated ‘FLATCANDY’ having an early season of maturity and which have fruits with high eating quality and very long shelf life without alteration before and after harvesting, with a semi-sweet white flesh with a red pigmentation, and a red pigmentation around the stone cavity, and an attractive skin with a very high percentage of purple red blush on skin surface, sometimes covering the whole surface or on a red background.